标题： 模算子的不变子模与Hilbert C*-模上的Lomonosov型定理 显示英文标题

标题： Invariant submodules of modular operators and Lomonosov type theorem for Hilbert C*-modules

摘要： 本文中，我们在Hilbert C*-模理论中引入了不变子模的概念，并研究了一些具有非平凡不变子模的有界可伴随算子及其广义逆的基本性质。 我们利用不变子模的优势来表示Hilbert C*-模上算子方程解集的表示。 特别是，我们将有限维C*-代数和紧算子的C*-代数作为基础C*-代数来简化我们的结果，并得到了某些Hilbert C*-模上紧算子的Lomonosov型定理。 显示英文摘要

摘要： In this paper, we introduce the notion of invariant submodule in the theory of Hilbert C*-modules and study some basic properties of bounded adjointable operators and their generalized inverses which have nontrivial invariant submodules. We demonstrate the representation of the solution set of an operator equation on Hilbert C*-modules by taking advantage of invariant submodules. In particular, we consider the special cases of finite dimensional C*-algebras and C*-algebras of compact operators as the underling C*-algebra to simplify our results, and obtain a Lomonosov type theorem for compact operators on some Hilbert C*-modules.